Abstract
The outer membrane (OM) of Gram-negative bacteria forms a protective barrier that combines selective permeability with mechanical load-bearing capacity, properties linked to its asymmetric bilayer structure with lipopolysaccharides (LPS) in the outer leaflet and phospholipids (PLs) in the inner leaflet. Unlike most PL bilayers, the OM typically exhibits limited lateral diffusion, resulting in a gel-like surface with spatially organized proteins and LPS. The molecular basis of this physical state and its relationship with envelope mechanics remain unclear. Here, we show that increasing PL levels in the outer leaflet or truncating LPS core oligosaccharides increases OM fluidity by disrupting LPS packing. In contrast, reduced LPS abundance or disruption of divalent cation-mediated crosslinking primarily reduces OM stiffness with little effect on fluidity. Thus, OM fluidity and mechanical stiffness can be tuned independently through distinct molecular interactions. This separation of physical control mechanisms provides a framework for understanding how Gram-negative bacteria modulate OM properties during environmental adaptation and envelope homeostasis.
Keywords: Outer membrane, fluidity, lipopolysaccharides, fluorescence recovery after photobleaching (FRAP), bamD, lipid asymmetry, waa genes, membrane mechanics
Introduction
The outer membrane (OM) of Gram-negative bacteria provides essential protection for growth and survival1. The OM is an asymmetric bilayer composed of lipopolysaccharides (LPS) in the outer leaflet, phospholipids (PLs) in the inner leaflet, and transmembrane β-barrel proteins that occupy a substantial fraction of the cell surface2. This architecture supports multiple functions, including acting as a permeability barrier and a mechanical load-bearing structure3. LPS in the outer leaflet restricts entry of potentially harmful molecules, including many antibiotics1,4,5. Complementing this chemical barrier, recent studies showed that the OM exhibits stiffness comparable to the rigid peptidoglycan (PG) cell wall, enabling it to resist mechanical stresses arising from changes in external osmolarity6. The OM is mechanically coupled to the cell wall by abundant linker molecules7–12, allowing the periplasm to function as an integrated mechanical unit that buffers turgor pressure during hypoosmotic shocks and tolerates osmolyte efflux from the cytoplasm13. During cell growth, the biogenesis of PG and the OM must therefore be coordinated to ensure synchronous expansion14,15. The OM also contributes to maintaining cell shape, as mutants with reduced OM protein levels exhibit morphological defects16, whereas strengthening the OM can restore rod shape in certain mutants with impaired cell wall synthesis17.
The physical properties of the OM are shaped by interactions among LPS, proteins, and PLs3,18–20. The OM exhibits pronounced spatial heterogeneity21–23 driven by preferential insertion of OM material at mid-cell24. This biased insertion is facilitated by inhibition of Bam complexes, which are responsible for OM protein insertion, by tetrapeptides present in mature PG near the cell poles15. As a result, newly synthesized OM components accumulate near the midcell while older proteins are displaced toward the poles24, generating spatial organization across the cell surface. Such patterning may promote turnover of OM proteins during growth24 and produce phenotypic heterogeneity between daughter cells25. At smaller scales, OM proteins form clusters visible via fluorescence microscopy21,24,26, while LPS-rich domains and lattice-like porin networks have been observed using atomic force microscopy2. Maintaining this spatial organization requires that surface molecules diffuse slowly enough to prevent homogenization by passive diffusion. Indeed, both OM proteins and LPS exhibit limited lateral mobility21,27–31, in contrast to the fluid-like behavior of most lipid bilayers, including the bacterial inner membrane (IM)32,33. Increased OM fluidity has been associated with compromised membrane integrity and increased permeability30,34–36, suggesting that permeability, fluidity, and mechanical strength may arise from common molecular interactions. However, despite the physiological importance of OM fluidity and spatial organization, the molecular mechanisms that determine OM fluidity, particularly how they relate to OM mechanics, remain poorly understood.
Here, we quantify LPS diffusion using fluorescence recovery after photobleaching (FRAP) of fluorescently labeled LPS (Methods)30,37. Because LPS constitutes a dominant component of the outer leaflet and coordinates the molecular interaction network at the OM surface, the lateral diffusion of labeled LPS provides a useful readout of the effective fluidity of the OM. Measuring LPS diffusion in Escherichia coli across a broad set of chemical and genetic perturbations revealed two distinct mechanisms controlling OM fluidity. Mutants with reduced levels of OM proteins exhibited large, growth-phase-dependent increases in fluidity associated with PL accumulation in the outer leaflet. In low-salt conditions, truncation of LPS core oligosaccharides also increased OM fluidity, likely by weakening intermolecular interactions between neighboring LPS molecules and disrupting their ordered packing. Strikingly, these perturbations altered OM fluidity without proportionally affecting OM stiffness. By contrast, reducing LPS abundance or acutely removing divalent cations that mediate LPS crosslinking strongly decreased OM stiffness while causing only modest changes in fluidity. Together, these results demonstrate that OM fluidity and mechanical stiffness can be tuned independently through distinct molecular interactions.
Results
PL accumulation increases LPS mobility
As an asymmetric bilayer rich in transmembrane porins and LPS, the OM exhibits physical properties distinct from those of the IM, likely arising from strong interactions among LPS and abundant OM proteins3. Previous studies showed that LPS crosslinking by divalent cations6 and the presence of OM proteins16 contribute to the load-bearing capacity of the E. coli OM. We therefore tested whether interactions among LPS and OM proteins determine OM fluidity, with stronger molecular interactions expected to reduce molecular mobility.
To quantify LPS diffusion, we measured fluorescence recovery using FRAP following metabolic labeling of LPS through an azide-alkyne reaction targeting 3-deoxy-D-manno-oct-2-ulosonic acid (Kdo) with Rhodamine 110 (Fig. 1a; Methods)30,37. Fluorescence recovery profiles of individual cells were compared with simulated one-dimensional diffusion profiles based on the initial photobleaching pattern to estimate diffusion coefficients (Fig. 1a; Methods).
Figure 1: Insertion of PLs into the outer leaflet fluidizes the OM by disrupting LPS packing.

a) Schematic of the FRAP assay used to measure LPS lateral diffusion. LPS molecules were labeled via Kdo-N3 incorporation and azide-alkyne click chemistry. FRAP was quantified by comparing experimental fluorescence recovery profiles to simulated one-dimensional diffusion profiles based on the diffusion equation (Methods).
b) ΔbamD and ΔbamD ΔpldA ΔmlaA cells, which have strongly reduced levels of OM proteins16, exhibit increased OM fluidity during log-phase and early stationary-phase growth in LB medium, as measured by the estimated LPS diffusion coefficient (Methods), coincident with PL accumulation in the OM outer leaflet. In late stationary phase (12 h), when PLs are removed from the outer leaflet, fluidity in ΔbamD cells returns to levels similar to the wild-type-like parent strain bamAE470K (gray), whereas fluidity remains elevated in ΔbamD ΔpldA ΔmlaA, which retain high PL levels. Upper: growth curves are shown as mean ± 1 standard deviation (s.d.) from three technical replicates. Lower: distributions of diffusion coefficients. Center line indicates medians, and error bars indicate the 25th and 75th percentiles. N > 15 cells were tested per condition.
c) Representative time-lapse images showing fluorescence recovery after photobleaching in bamAE470K, ΔbamD, and ΔbamD ΔpldA ΔmlaA cells at different growth phases in LB medium. Scale bar: 2 μm.
d) OM fluidity is increased in log-phase mlaA* ΔpldA cells grown in LB, which accumulate PLs in the outer leaflet without direct disruption of OM protein assembly. Center lines indicate medians, and error bars indicate the 25th and 75th percentiles. N > 17 cells were tested per condition.
e) Model illustrating OM fluidization caused by PL accumulation in the outer leaflet. Increased PL content, resulting from reduced OM protein levels or enhanced PL flux, disrupts the tight packing of LPS molecules.
To investigate the contribution of OM proteins in OM fluidity, we examined a previously characterized ΔbamD mutant. Deletion of bamD causes a global reduction in OM proteins, with PLs filling the resulting void by flipping from the inner leaflet to the outer leaflet during log-phase growth16. In stationary phase, the ΔbamD OM becomes mechanically destabilized due to the activities of OM phospholipase A and the Mla system38–43, which remove PLs from the outer leaflet and eventually cause OM rupture in a fraction of cells16. Thus, outer-leaflet PL levels are expected to increase during growth and decrease in stationary phase. Consistent with this model, ΔbamD cells (Table S1) exhibited a ~1000-fold increase in LPS diffusion after 6 h of growth in LB medium (early stationary phase) compared with cells immediately back-diluted from a 12-h culture representing late stationary phase and the onset of regrowth (Fig. 1b,c). Fluorescence recovery kinetics closely resembled normal diffusion (Fig. S1). In contrast, the bamAE470K parent strain exhibited similarly low LPS diffusion across growth phases, comparable to late stationary-phase ΔbamD cells (Fig. 1b,c).
These growth phase-dependent changes in OM fluidity in ΔbamD cells mirrored previously characterized dynamics of PL accumulation in the outer leaflet during log phase and subsequent PL removal during stationary phase16, suggesting that outer-leaflet PL abundance is an important determinant of OM fluidity. To test this hypothesis, we quantified LPS diffusion in a ΔbamD ΔpldA ΔmlaA mutant (Table S1), in which loss of PldA-mediated PL degradation and Mla-dependent PL removal promotes retention of PLs in the OM outer leaflet16. In this triple mutant, OM fluidity remained high across all growth phases (Fig. 1b). Further supporting this interpretation, a ΔbamB mutant, which has a milder defect in OM protein folding than ΔbamD44,45, exhibited intermediate, growth phase-dependent OM fluidization (Fig. S2), consistent with lower levels of PL accumulation in the outer leaflet.
Because ΔbamD simultaneously reduces OM protein abundance and increases outer-leaflet PLs, we next asked whether PL accumulation could increase OM fluidity without direct disruption to OM protein assembly. Unlike bam mutants, which disrupt the BAM complex and globally reduce OMP levels, the gain-of-function allele mlaA* primarily perturbs lipid asymmetry by promoting PL accumulation in the outer leaflet46. In an mlaA* ΔpldA mutant, in which PLs are driven into and retained in the outer leaflet, OM fluidity was high (Fig. 1d). This is consistent with the disruption of LPS-OM protein packing in ΔmlaA ΔpldA cells previously observed using atomic force microscopy2. These results demonstrate that outer-leaflet PL accumulation can drive increased LPS diffusion even when the primary perturbation does not directly disrupt OM protein assembly, supporting PL-mediated disruption of LPS packing as a major determinant of OM fluidization.
LPS core oligosaccharides restrict OM fluidity under low-salt conditions
LPS is an amphipathic molecule composed of a lipid moiety (lipid A), core oligosaccharides, and, in some strains, a long polysaccharide chain termed the O-antigen47 (in most E. coli laboratory strains, including the K-12-derived strains used in this study, the O-antigen is absent). LPS contains multiple negatively charged phosphate groups that promote formation of an ordered LPS network through salt bridges mediated by divalent cations20. Core oligosaccharides further mediate interactions between LPS molecules and contribute to OM mechanical stiffness48.
Based on this structure, we hypothesized that shortening the core oligosaccharides would weaken interactions between neighboring LPS molecules and thereby increase OM fluidity relative to wild-type cells. To test this hypothesis, we measured LPS diffusion in mutants defective in core oligosaccharide synthesis (Fig. 2a,b and S3). The waa genes encode enzymes that sequentially catalyze addition of sugars to the LPS core49, and deletion of specific waa genes produces LPS molecules truncated to varying extents.
Figure 2: OM fluidity depends on the length of LPS core oligosaccharides.

a) Genetic truncation of LPS core oligosaccharides progressively increased OM fluidity in NaCl-deficient MHB medium, with the magnitude of the effect depending on the remaining oligosaccharide length. Cells were grown for 3 h prior to measurement. Center lines indicate medians, and error bars indicate the 25th and 75th percentiles. N > 18 cells were tested per condition. p values were calculated using Welch’s t-test on log10-transformed diffusion coefficients. ***: p < 0.001; *: p < 0.05; n.s.: p > 0.05.
b) Representative time-lapse images showing fluorescence recovery after photobleaching in wild-type, ΔwaaF, ΔwaaD, and ΔwaaG cells grown in MHB.
c) OM fluidity was largely independent of growth phase in ΔwaaF and ΔwaaG cells, with no statistically significant differences detected across time points. Center lines indicate medians, and error bars indicate the 25th and 75th percentiles. N > 14 cells were tested per condition. p values were calculated using Welch’s t-test on log10-transformed diffusion coefficients. ***: p < 0.001; n.s.: p > 0.05.
d) Supplementation of MHB with 1% NaCl or 340 mM sorbitol (osmotically equivalent to 1% NaCl) restored low OM fluidity in ΔwaaD cells. Growth in LB (Lennox; 0.5% NaCl) partially restored low fluidity. Diffusion coefficients are shown as box plots; center lines indicate medians, and error bars indicate the 25th and 75th percentiles. N > 16 cells per condition. p values were calculated using Welch’s t-test on log10-transformed diffusion coefficients. ***: p < 0.001; *: p < 0.05; n.s.: p > 0.05.
A previous study reported that ΔwaaD exhibits increased diffusion of fluorescent pyrenedecanoic acid probes incorporated into the OM when cells are grown in the low-salt rich medium MHB, compared to MHB supplemented with 1% NaCl50. Motivated by this observation, we quantified LPS diffusion in waa mutants51 (Table S1) grown in MHB. Consistent with a model in which reduced LPS-LPS interactions increase OM fluidity, the extent of fluidization depended on the remaining length of the core oligosaccharides (Fig. 2a,b). ΔwaaD and ΔwaaF mutants, which possess the shortest inner cores52–54, exhibited the highest fluidity (Fig. 2a), whereas ΔwaaJ, whose LPS structure is only modestly truncated, showed no significant increase (Fig. 2a). These results suggest that longer core oligosaccharides restrict LPS mobility, potentially by strengthening interactions between neighboring LPS molecules.
ΔwaaP cells also exhibited increased fluidity, which may reflect loss of phosphate groups and/or impaired synthesis of the outer core55. Unlike the bam mutants, increased OM fluidity in ΔwaaF and ΔwaaG cells was independent of growth phase (Fig. 2c), consistent with weakened interactions between truncated core oligosaccharides rather than growth phase-dependent PL insertion into the outer leaflet.
Environmental salt conditions strongly influenced these effects. In LB (Lennox) or MHB supplemented with 1% NaCl, ΔwaaD cells exhibited substantially lower fluidity than in unsupplemented MHB (Fig. 2d), consistent with previous observations of salt dependence in wild-type cells50. This reduction could arise either from ionic effects that strengthen LPS-LPS interactions or from increased environmental osmolarity. To distinguish between these possibilities, we measured LPS diffusion in NaCl-deficient MHB supplemented with 340 mM sorbitol, which matches the osmotic strength of MHB+1% NaCl without introducing additional ions. Sorbitol restored low fluidity (Fig. 2d), indicating that the effects of NaCl arise primarily from increased external osmolarity rather than ionic interactions alone. These results suggest that higher osmolarity restricts LPS diffusion, consistent with increased packing or confinement of OM components.
To understand how truncation of LPS core oligosaccharides affects LPS motility and spatial packing, we performed all-atom molecular dynamics (MD) simulations of OM patches containing 34 LPS molecules derived from either wild-type or ΔwaaF cells (Fig. S4a; Methods). These simulations revealed that LPS oligosaccharides interact primarily through direct hydrogen bonds and crosslinking mediated by divalent cations (Fig. 3a,c). Truncation of the core oligosaccharides reduced these interactions (Fig. 3b,d), relieving local confinement of LPS molecules and increasing local mobility (Fig. 3e,f). Although the simulation timescale (5 μs) was much shorter than the estimated time (~1 ms) required for an LPS molecule with diffusion constant D~10−3 μm2/s to traverse a distance comparable to its lateral size (~1.5 nm), diffusion coefficients estimated from mean-squared displacement were consistent with experimentally measured values (Fig. S4b,c; Methods).
Figure 3: Truncation of LPS core oligosaccharides weakens intermolecular interactions, disrupts packing, and increases local mobility in MD simulations.

a) Representative LPS molecule and hydrogen bonds with its six nearest neighbors in wild-type and ΔwaaF systems. Truncated ΔwaaF LPS forms fewer hydrogen bonds with neighboring LPS molecules. Each LPS is shown in a different color, and thick red lines denote hydrogen bonds.
b) Truncation reduces the number of hydrogen bonds formed by individual LPS molecules with neighboring LPS, quantified over the final 1 μs of simulation. Each violin plot represents an independent simulation. Data points correspond to individual LPS molecules; center lines indicate medians, and error bars indicate the 25th and 75th percentiles.
c) Representative LPS molecules and associated divalent cations in wild-type and ΔwaaF systems. Mg2+ and Ca2+ ions within 4 Å of LPS are shown, illustrating reduced association of divalent cations with truncated LPS.
d) Truncation reduces the number of divalent cations associated with individual LPS molecules over the final 1 μs of simulation, illustrating the weakening of interactions that stabilize neighboring LPS molecules. Violin plots show distributions for individual LPS molecules in each independent simulation; center lines indicate medians, and error bars indicate the 25th and 75th percentiles.
e) Two-dimensional center-of-mass (COM) trajectories during the final 1 μs of simulation of lipid A for a representative LPS molecule and its six nearest neighbors, as determined from the initial configuration. The greater spatial excursions in ΔwaaF illustrate increased local motion following core truncation.
f) Truncated ΔwaaF LPS exhibits increased local lateral motion, reflected by higher root-mean-square fluctuation (RMSF) of lipid A COM positions over the final 1 μs of simulation. Data points correspond to individual LPS molecules; center lines indicate medians, and error bars indicate the 25th and 75th percentiles. Two independent simulations were analyzed for each genotype.
g) LPS core truncation reduces local packing order. Time courses of the mean local hexatic order parameter, , which reports the angular organization of nearest neighbors around each LPS molecule (Methods), show that wild-type and ΔwaaF LPS relax into distinct packing states, with ΔwaaF maintaining lower local order. Shaded regions indicate the initial and final 50-ns intervals used to illustrate the distributions at right.
h) Time-averaged local hexatic order for individual LPS molecules over the final 1 μs of simulation, , confirms reduced local packing order in ΔwaaF relative to wild type. Data points correspond to individual LPS molecules; center lines indicate medians, and error bars indicate the 25th and 75th percentiles.
i) Representative endpoint configurations of wild-type and ΔwaaF LPS layers colored by local , illustrating the greater local packing order of wild-type LPS. Circles indicate molecules within the primary simulation box and squares indicate periodic images. Insets show representative central LPS molecules and their nearest-neighbor networks, with solid and dashed lines representing the configuration at t=4.5 μs and a perfect hexagonal lattice, respectively.
j) Core truncation accelerates rearrangement of local LPS neighborhoods. The fraction of the original six nearest neighbors retained around each LPS molecule decreases more rapidly in ΔwaaF than in wild-type, indicating that intact core oligosaccharides stabilize local LPS coordination shells and restrict neighbor exchange.
We next tested whether weakened interactions disrupt the organization of the LPS layer. In wild-type simulations, LPS molecules formed locally ordered hexagonal arrays, whereas ΔwaaF simulations showed more disordered configurations across independent simulations (Fig. 3g-i), quantified by a lower local hexatic order parameter measuring nearest-neighbor angular alignment (Methods). Packing disruption also propagated to larger scales: ΔwaaF LPS exhibited reduced long-range order, reflected in a lower global hexatic order parameter (Fig. S4d; Methods). To assess whether structural disorder was associated with a more dynamic local environment, we tracked neighbor exchange over time (Methods). Intermolecular contacts persisted significantly longer in wild-type simulations (Fig. 3j), demonstrating that core truncation destabilizes the local LPS lattice and accelerates molecular rearrangement. Together, these results indicate that intact core oligosaccharides stabilize local LPS organization by enhancing packing order and suppressing rapid molecular rearrangement, likely within a broader OMP-LPS interaction network.
OM fluidity is largely insensitive to LPS abundance or divalent-cation crosslinking
Because LPS is a prominent component of the OM outer leaflet, reductions in LPS abundance might be expected to weaken intermolecular interactions and thereby increase OM fluidity. To test this possibility, we examined mutants with impaired LPS transport. LPS is synthesized in the cytoplasm and transported to the OM via the Lpt system56. The imp4213 allele of lptD reduces LPS transport by impairing the function of LptD44,45, which together with LptE inserts LPS into the OM. Although imp4213 (Table S1) reduces OM stiffness6 and increases permeability44,45, we observed only minimal increases in LPS diffusion in LB (Fig. 4a) and modest (~10-fold) increases in MHB (Fig. S5). In imp4213 cells, decreased LPS transport renders the OM permeable to hydrophobic compounds44 due to the formation of PL-rich domains that likely explain the modest increase in fluidity. Similarly, CRISPRi inhibition of LPS transport (lptC) or synthesis (lpxC; Table S1) resulted in only slight increases in fluidity (Fig. 4a) despite large reductions in LPS levels, in contrast to the substantial fluidization caused by bamD deletion (Fig. 1b).
Figure 4: Disrupting LPS crosslinking or reducing LPS levels causes only modest increases in OM fluidity.

a) Reducing LPS levels through the imp4213 allele or CRISPRi inhibition of lpxC or lptC results in only modest increases in OM fluidity compared with PL accumulation in the OM outer leaflet (ΔbamD ΔpldA ΔmlaA cells). Center lines indicate medians, and error bars indicate the 25th and 75th percentiles. N > 12 cells were tested per condition. p values were calculated using Welch’s t-test on log10-transformed diffusion coefficients. ***: p < 0.001; **: p < 0.01; n.s.: p > 0.05.
b) Chelation of divalent cations with EDTA produces a smaller increase in OM fluidity than truncation of LPS core oligosaccharides or reduction of OM proteins. Cells were grown in LB for 3 h to mid-log phase prior to EDTA treatment. Center lines indicate medians, and error bars indicate the 25th and 75th percentiles. N > 17 cells were tested per condition. p values were calculated using Welch’s t-test on log10-transformed diffusion coefficients. ***: p < 0.001; n.s.: p > 0.05.
In a previous study, we showed that divalent-cation crosslinking of LPS is critical for OM rigidity6. To test whether this crosslinking also restricts OM fluidity, we measured LPS diffusion in wild-type cells following treatment with high concentrations of EDTA (Methods). Chelation of divalent cations with EDTA concentrations up to 50 mM resulted in only minor increases in OM fluidity in either LB or MHB (Fig. 4b and S5), even though such concentrations reduce OM stiffness by more than 60%6. Supplementation with 50 mM MgCl2 in LB failed to restore low fluidity in ΔbamD cells (Fig. S6), further indicating that the mechanism underlying increased LPS diffusion in ΔbamD is largely independent of LPS crosslinking. The differential effects of EDTA treatment (Fig. S5) and inner core oligosaccharide truncation (Fig. 2a) on LPS diffusion suggest that distinct LPS intermolecular interactions control OM fluidity and OM mechanical stiffness.
OM fluidity and stiffness are independently tunable
Our results indicate that although OM fluidity and stiffness both arise from interactions among porins, LPS, and PLs in the outer leaflet, these physical properties can be modulated independently. For instance, growing ΔbamB cells exhibited a 10-fold increase in OM fluidity (Fig. S2) while maintaining wild-type stiffness16. Conversely, the imp4213 mutation and EDTA treatment each reduce OM stiffness6 but did not increase fluidity (Fig. 4).
To systematically compare these properties across perturbations, we organized fluidity and stiffness measurements from this and our previous studies6,16 into a phenomenological map (Fig. 5a). This analysis revealed distinct trends associated with perturbations affecting OM proteins and PL levels versus those altering LPS abundance or divalent-cation interactions. Notably, mlaA* ΔpldA cells retained substantial stiffness (Fig. 5a) despite markedly increased OM fluidity (Fig. 1d). Similarly, CRISPRi knockdown of bamD (Table S1) progressively increased LPS diffusion as PLs accumulated in the outer leaflet due to defective OM protein insertion, without reducing stiffness (Fig. 5a), consistent with the behavior of ΔbamB (Fig. S2)16. In contrast, perturbations that reduce LPS levels or chelate divalent cations decreased stiffness without substantially altering fluidity (Fig. 5a).
Figure 5: OM fluidity and stiffness can be modulated independently by perturbations to OM proteins and LPS.

a) Phenomenological map comparing OM fluidity and stiffness across perturbations affecting OM composition. The imp4213 allele, chelation of divalent cations by EDTA (which reduces LPS crosslinking and extracts LPS from the OM77), or knockdown of either lpxC or lptC reduced OM stiffness without substantially increasing fluidity. In contrast, ΔbamB cells exhibit increased fluidity while OM stiffness remains similar to wild type16. CRISPRi knockdown of bamD increased fluidity in an induction time-dependent manner under steady-state exponential growth conditions without substantially reducing stiffness. Similarly, mlaA* ΔpldA cells exhibited high fluidity while retaining near-wild-type-level stiffness. LPS core truncation mutants (waa mutants) grown in MHB showed increased fluidity accompanied by a modest reduction in stiffness. All fluidity measurements were obtained in this study. OM stiffness values for imp42136, EDTA-treated wild-type6, bamAE470K16, and ΔbamB16 cells were reported previously, whereas all other stiffness measurements were performed in this study. Mutant stiffness values were normalized to their corresponding wild-type strain, parent strain, or no-induction control. Circles indicate medians, and error bars indicate the 25th and 75th percentiles of LPS diffusion coefficients. Error bars are not shown for stiffness, as values were calculated from averaged cell length contractions (Methods).
b) Schematic illustrating the changes in OM composition, organization, and molecular interactions that underlie the stiffness and fluidity regimes in the corresponding quadrants of the fluidity-stiffness map in a). Reducing OM protein levels promotes PL intercalation between LPS molecules, weakening LPS packing and increasing LPS fluidity. However, PL accumulation resulting from reduced OM protein levels is insufficient to disrupt the continuity of the LPS-LPS interaction network that supports load bearing across the cell length. In contrast, replacing LPS with PLs likely disrupts this LPS interaction network and yields a more continuous OMP-PL matrix with limited load-bearing capacity, while the increased OMP to LPS ratio may still restrict LPS diffusion through steric confinement and/or LPS-OMP interactions.
Together, these results indicate that membrane composition influences OM properties through separable mechanisms, revealing two largely independent control knobs (Fig. 5a). Abundant LPS, stabilized by divalent cations, contributes strongly to the load-bearing capacity of the OM. When OM proteins are gradually replaced by PLs, the OM can retain near-wild-type stiffness even as PL accumulation fluidizes LPS, implying that the LPS network continues to bear most of the mechanical load as PLs incorporate into the outer leaflet. In contrast, conditions that reduce LPS abundance or disrupt cation-mediated stabilization decrease stiffness without a commensurate increase in LPS mobility. Under these conditions, porins may still restrain LPS motion within a PL-enriched outer leaflet, potentially through LPS-porin interactions.
The fluidity-stiffness map (Fig. 5a) also reveals distinct contributions from different structural features of LPS. Chelation of divalent cations with EDTA reduced stiffness without affecting fluidity, whereas truncation of the core oligosaccharides (waa mutants) progressively increased LPS mobility with only modest decreases in stiffness (Fig. 5a). These trends indicate that the core oligosaccharides contribute primarily to restricting lateral mobility, whereas divalent-cation-mediated salt bridges contribute more strongly to OM mechanical rigidity.
Discussion
In this study, we used FRAP assays of fluorescently labeled LPS to quantify effective OM fluidity and identify molecular interactions that control LPS mobility. Across a wide range of genetic and chemical perturbations, PL insertion into the outer leaflet and truncation of LPS oligosaccharides markedly increased OM fluidity, whereas perturbations that reduce LPS levels or chelate divalent cations primarily weakened OM stiffness. These findings indicate that OM fluidity and stiffness can be modulated independently through distinct molecular interactions, challenging the intuition that low fluidity and high stiffness are tightly coupled and highlighting multiple molecular targets for tuning OM physical properties. Further elucidating these mechanisms will deepen our understanding of OM organization and maintenance and may ultimately reveal novel strategies for destabilizing the OM. Throughout this study, we use lateral diffusion of LPS as a readout of effective OM fluidity. Although this measurement reports specifically on LPS mobility, the central role of LPS in mediating intermolecular interactions within the membrane means that changes in LPS mobility reflect changes in the physical state of the OM surface.
Using fluidity as a readout of intermolecular interactions, our study reveals architectural features that shape OM organization. Our data suggest that when PLs replace proteins in the outer leaflet, they intercalate among LPS molecules and weaken interactions that normally constrain LPS mobility. We did not observe heterogeneous fluorescence patterns in ΔbamD cells (Fig. 1c), at least at the diffraction-limited scale, suggesting that PL accumulation does not produce obvious micron-scale segregation of LPS-rich and PL-rich regions, although we cannot exclude nanoscale domains below the diffraction limit. LPS core truncation reveals a distinct mechanism for disrupting LPS packing. In atomistic simulations, truncation reduced direct hydrogen bonding and divalent cation-mediated interactions between neighboring LPS molecules, increased local fluctuations, disrupted both local and long-range packing order, and accelerated nearest-neighbor exchange (Fig. 3, S4). These results suggest that intact core oligosaccharides stabilize transient local coordination shells that confine neighboring LPS molecules and limit lateral rearrangement. Core truncation weakens these coordination shells, providing a molecular explanation for the increased LPS mobility observed experimentally.
The increase in fluidity caused by reductions in LPS levels and corresponding PL accumulation (Fig. 4a) did not phenocopy the fluidization caused by replacement of proteins with PLs (Fig. 1), potentially because abundant OM proteins interact with and restrict LPS mobility or act as large obstacles that divide the membrane surface into inter-porin channels that limit diffusion (Fig. 5b). Consistent with this idea, OMP-LPS arrangements observed in wild-type cells may create locally confined populations of LPS alongside more mobile regions, as suggested by previous descriptions of porin-LPS organization in the OM2,24. Thus, disruption of LPS packing emerges as a major driver of OM fluidization, while OMPs may modulate LPS mobility through steric confinement or specific LPS-protein interactions, without being the primary determinant of LPS diffusion under the conditions tested. Consistent with this interpretation, across perturbations where OM protein levels differ substantially (bamAE470K versus ΔbamD), the largest shifts in LPS diffusion coincide with conditions known to alter outer-leaflet PL content. Moreover, LPS mobility is high in mlaA* ΔpldA cells, in which the primary perturbation drives PL accumulation rather than directly disrupting OM protein assembly. Together, these observations demonstrate that increased outer-leaflet PL abundance can drive large increases in LPS mobility without directly disrupting OM protein assembly, supporting PL-mediated disruption of LPS packing as a major determinant of OM fluidization.
In contrast to fluidity, OM stiffness reflects the ability of the membrane to resist in-plane stress and, as our data suggest, is more sensitive to reductions in LPS than to reductions in OM proteins (Fig. 5a). We propose that maintaining stiffness requires a laterally continuous network of LPS-LPS interactions spanning the cell surface, reinforced primarily by divalent-cation bridges between neighboring LPS molecules (Fig. 5b). When PLs replace OM proteins, they partially disrupt local LPS packing but apparently do not fragment the LPS interaction network into mechanically disconnected regions, allowing the membrane to retain near-wild-type stiffness even as lateral mobility increases. In contrast, when PLs replace LPS, the combined decrease in LPS abundance and emergence of a more continuous OMP-PL matrix may more readily break apart the LPS interaction network. Because such an OMP-PL mixture is unlikely to sustain in-plane compression as effectively as an LPS-rich network, stiffness decreases even when lateral mobility remains constrained.
The decoupling of OM fluidity and stiffness has important implications for the structural and functional versatility of Gram-negative bacteria. Our findings suggest that while a rigid, crosslinked LPS network primarily provides mechanical strength, shifts in the balance between OM proteins and PLs modulate lateral mobility. This separation creates opportunities for bacteria to tune OM physical properties to meet diverse functional demands and environmental conditions. It is therefore likely that regulatory pathways adjust OM composition to maintain appropriate mechanical and diffusive properties. Measuring these properties across varying growth conditions, including growth phases, growth rate, and temperature, may reveal mechanisms of envelope homeostasis. In addition, structural variation in the OM across species may produce distinct mechanical and diffusive behaviors. For example, Vibrio cholerae has a much weaker OM than the load-bearing OM of E. coli or Pseudomonas aeruginosa6, raising the possibility that OM fluidity also varies across species according to ecological niche.
The OM contains abundant structural porins but relatively few enzymes, possibly reflecting constraints imposed by low lateral fluidity on surface-embedded catalysis. Nevertheless, several OM-associated enzymes could respond to and potentially regulate OM fluidity. PldA hydrolyzes PLs mislocalized to the outer leaflet57, while PagP transfers palmitate from PLs to lipid A in response to elevated outer-leaflet PL levels58. Because the activities of both enzymes are linked to disrupted lipid asymmetry, the increased fluidity accompanying PL accumulation could influence their access to membrane substrates. Such coupling between OM physical state and enzymatic activity could provide a feedback mechanism that helps restore lipid asymmetry and maintain envelope homeostasis.
Methods
Culture conditions for LPS staining
E. coli cells were grown overnight at 37 °C in M9 minimal medium supplemented with 0.2% glucose (Sigma-Aldrich, Cat. #G8270) and 0.5% casamino acids (RPI, Cat. #C45000). Overnight cultures were diluted 1:1000 into fresh M9 medium containing 5 mM 8-azido-3,8-dideoxy-D-manno-octulosonic acid (Kdo-N3, WuXi AppTec) and incubated overnight under the same conditions. The resulting saturated cultures were diluted 1:200 into lysogeny broth (LB, RPI, Cat. #L24060) or Mueller Hinton Broth (MHB, BD Difco, Cat. #212322) supplemented with 5 mM Kdo-N3 and grown for the indicated durations before LPS staining and FRAP measurements. For ΔbamD strains, cultures were diluted 1:50 due to the lower optical density (OD) reached in saturated cultures.
LPS labeling via azide–alkyne click chemistry
LPS molecules were labeled using a copper-catalyzed azide–alkyne cycloaddition reaction adapted from a published protocol37. A catalyst buffer was prepared by mixing 2 mM CuSO4 (Sigma-Aldrich, Cat. #31293) and 4 mM tris(6-galactosyltriazomethyl)amine (TGTA, WuXi AppTec)61 in 50 mM sodium phosphate (Sigma-Aldrich, Cat. #8210-OP) buffer (pH 7.5) and incubating overnight at 37 °C with shaking. To prepare the labeling mixture, the catalyst buffer was supplemented with 4 mM aminoguanidine HCl (Sigma-Aldrich, Cat. #396494), 5 mM sodium ascorbate, and 130 μM rhodamine 110-PEG4-alkyne (Sigma-Aldrich, Cat. #761621). Cells cultured in the presence of Kdo-N3 were washed three times with 50 mM sodium phosphate buffer, incubated with the labeling mixture for 10 min at room temperature, and then washed twice with sodium phosphate buffer before resuspension in the same buffer for FRAP measurements.
Fluorescence recovery after photobleaching (FRAP) assays
One microliter of cells with fluorescently labeled LPS was placed onto a 1% agarose pad prepared with 0.85X PBS (Gibco, Cat. #70011044), which has approximately the same osmolarity as LB medium. Samples were imaged using a Zeiss LSM880 inverted laser-scanning confocal microscope equipped with a 63X oil-immersion objective. A manually defined region of the cell, typically near midcell, was photobleached by repeated high-intensity laser scanning. Fluorescence recovery within the bleached region was then monitored for 30 s to 3 min, depending on the recovery kinetics. Images were acquired using Zeiss ZEN software. All imaging was performed at 37 °C using an environmental chamber with active temperature control.
FRAP analysis
Time-lapse fluorescence images were segmented using the software Morphometrics62 to extract cell contours at sub-pixel resolution. These contours were processed using the meshing algorithm from MicrobeTracker63 and MATLAB (R2025b) to determine the cell centerline along the major axis and generate a one-dimensional fluorescence intensity profile along the cell length. To quantify membrane fluidity, these fluorescence recovery profiles were compared to simulated one-dimensional diffusion curves with zero-flux boundary conditions, and the diffusion coefficient was extracted via linear fitting (Fig. 1a).
For each cell, the dynamics of the one-dimensional fluorescence profile for , where denotes cell length, were simulated using the diffusion equation with zero-flux boundary conditions:
with initial condition
and boundary conditions
The diffusion equation was solved using the implicit backward Euler method.
The progress of fluorescence recovery was quantified using a normalized recovery metric , where . This metric was defined as the normalized L1-norm difference between the fluorescence profile at time and the profile corresponding to complete equilibration of labeled molecules after long diffusion times (Fig. S1a and S3a), i.e.,
For linear diffusion, is predicted to converge approximately exponentially from 0 to 1. For FRAP experiments, the long-time profile was approximated by the pre-photobleaching fluorescence profile corrected for total fluorescence loss due to photobleaching. For simulations, the long-time profile was defined as uniform with the same total fluorescence as the post-photobleaching profile.
For each cell, experimental FRAP recovery profiles were first normalized to the total fluorescence immediately after photobleaching and then compared to a series of simulated profiles with sufficient temporal resolution to densely cover recovery values from 0 to 0.99. Simulations were performed using a standard diffusion coefficient of and a normalized length of 1 μm (the cell length was later scaled to the experimentally measured value).
The difference between each experimental and simulated profile was calculated as
which was then normalized to obtain a similarity matrix :
To determine the experimental diffusion coefficient, a linear regression was performed using all () data pairs weighted by . The resulting slope was then used to scale the standard diffusion coefficient to the experimental coefficient as
Because this method relies on comparing fluorescence recovery between experiments and simulations, it effectively covers diffusion rates above 10−4 μm2/s. For slower diffusion, corresponding to characteristic timescales greater than 104 s, fluorescence recovery is negligible within the observation window (~2–3 min), resulting in low signal-to-noise ratios and inaccurate estimates of diffusion coefficients. In such cases, LPS fluidity is effectively immobile relative to physiologically relevant timescales such as the 20–60 min doubling time in standard culture media.
To assess deviations from ideal linear diffusion, we compared experimental recovery with simulated recovery for each cell (Fig. S1b and S3b). Cells with data points falling along the diagonal of the plot exhibited kinetics consistent with linear diffusion, whereas cells with convex deviations toward the axis showed progressively slowing recovery, potentially reflecting subpopulations of less mobile LPS molecules.
To estimate the fraction of immobile LPS in each cell, the measured recovery curve was fitted to
where and represent the fraction of mobile LPS and the characteristic recovery timescale, respectively (Fig. S1c and S3c). This analysis assumes that the mobile LPS population follows approximately normal diffusion, which was largely supported under the conditions tested in this study (Fig. S1 and S3).
OM stiffness measurements
Stiffness was quantified using a microfluidic plasmolysis-lysis assay as previously described6. Steady-state log-phase cells grown in LB or MHB with 300 μM 3-[[(7-hydroxy-2-oxo-2H-1-benzopyran-3-yl)carbonyl]amino]-D-alanine hydrochloride (HADA, MedChemExpress, Cat. #HY-131045/CS-0124027) were loaded into a CellASIC ONIX microfluidic flow cell (Sigma-Aldrich, Cat. #B04A-03–5PK) and incubated for 30 min at 37 °C in the corresponding medium containing HADA. Cells were then perfused with 0.85X PBS, subjected to a hyperosmotic shock with 1 M sorbitol (Sigma-Aldrich, Cat. #S6021) in 0.85X PBS, and subsequently treated with 5% (w/v) N-lauroylsarcosine sodium salt (MP biomedicals, Cat. #190289) in 1 M sorbitol and 0.85X PBS as a detergent to remove the membranes. Media exchanges were performed using the CellASIC ONIX2 microfluidic platform (Sigma-Aldrich, Cat. #CAX2-S0000). Cells were imaged using a Nikon Eclipse Ti-E inverted fluorescence microscope equipped with a 100X oil-immersion objective (NA 1.40; Nikon Instruments). Phase-contrast and fluorescence images were acquired with a Prime BSI Express sCMOS camera (Teledyne Photometrics) to monitor cell morphology. All imaging was conducted at 37 °C using an environmental chamber with active temperature control (HaisonTech).
Images of HADA-labeled cells were segmented using the machine-learning-based software DeepCell64 and analyzed with Morphometrics to extract single-cell contours. Because HADA is sensitive to photobleaching, images were acquired at a relatively low frame rate (one frame every 1–5 min). Cell lineages were therefore reconstructed by manual curation for a representative subset of cells. Cell length and width were calculated from the contours using the MicrobeTracker meshing algorithm.
Cell wall lengths were measured in the turgid state , under plasmolysis , and after OM removal . Length contractions between these states were calculated as , and . The OM stiffness relative to the cell wall stiffness was estimated using the average length contractions according to , where denotes the mean of the indicated quantity, as previously described6.
CRISPR knockdown
EZ rich defined medium (EZ-RDM) was prepared by combining 100 mL of 10X MOPS buffer (Teknova, Cat. #M2101), 100 mL of 10X ACGU solution (Teknova, Cat. #M2103), 10 mL of 0.132 M K2HPO4 (Sigma-Aldrich, Cat. #PX1570), and 200 mL of 5X supplemented EZ (Teknova, Cat. #M2104) with 580 mL of water65. The medium was supplemented with 0.2% glycerol (Sigma-Aldrich, Cat. #GX0190).
lpxC and lptC CRISPRi strains were cultured and induced following a previously established protocol66 with minor modifications for LPS labeling. For FRAP assays, cells were grown overnight at 37 °C in M9 minimal medium, diluted 1:1000 into fresh M9 medium containing 5 mM Kdo-N3, and grown overnight under the same conditions. The resulting culture was diluted 1:200 into EZ-RDM supplemented with 0.2% glycerol and 5 mM Kdo-N3 and grown for 3 h to mid-log phase. Knockdown was induced by adding 0.2% L-arabinose (Sigma-Aldrich, Cat. #A91906) and cells were harvested after 90 or 150 min for FRAP measurements.
For OM stiffness measurements, cells were grown overnight at 37 °C in EZ-RDM supplemented with 0.2% glycerol, diluted 1:200 into fresh EZ-RDM, and grown for 3 h before being loaded into a CellASIC flow cell. In the flow cell, knockdown was induced with 0.2% L-arabinose in EZ-RDM for 90 or 150 min before plasmolysis with 1 M sorbitol in 0.85X PBS and lysis with 5% N-lauroylsarcosine sodium salt. For these experiments, 25 μg/mL wheat germ agglutinin (WGA) Alexa Fluor 488 (Invitrogen, Cat. #W11261), rather than HADA, was used throughout the experiment to achieve improved cell envelope staining.
The bamD CRISPRi strain was obtained from a previously generated CRISPR interference library67 and cultured and induced according to the established protocol67 with minor modifications for LPS labeling. For FRAP assays, cells were grown overnight at 37 °C in M9 minimal medium, diluted 1:1000 into fresh LB containing 5 mM Kdo-N3, and grown overnight under the same conditions. The resulting culture was diluted 1:200 into LB containing 5 mM Kdo-N3 and grown for 3 h to mid-log phase. Knockdown was induced by adding IPTG to a final concentration of 1 mM, and cultures were maintained in exponential growth by serial dilution for 9 h. Cells were harvested for FRAP measurements at 0 min, 150 min, 6 h, and 9 h after induction.
Molecular dynamics simulations
All-atom models of the E. coli K-12 OM were constructed using CHARMM-GUI68,69. The native membrane composition consisted of an outer leaflet containing 100% homogeneous LPS molecules and an inner leaflet composed of 90% PVPE, 5% PVPG, and 5% PVCL2 lipids70,71. Each membrane patch contained 34 LPS molecules in the outer leaflet. Each system was solvated in 0.15 M KCl, and LPS molecules were neutralized with Mg2+ and Ca2+ ions. Simulations were performed using the CHARMM36 all-atom force field72 and NAMD3 molecular dynamics software73. Production simulations employed hydrogen mass repartitioning to enable a 4 fs integration timestep74. Bonds involving hydrogen were constrained. Van der Waals interactions were smoothly switched to zero between 10 and 12 Å. Long-range electrostatics were treated using the particle mesh Ewald method with a grid spacing of 1.0 Å. Simulations were carried out under periodic boundary conditions at 310 K and 1 atm using Langevin dynamics with a damping coefficient of 1 ps−1 and the Langevin piston method. Semi-isotropic pressure coupling was used to allow independent fluctuations of the membrane plane and bilayer normal. Two independent replicas were simulated for each system, yielding two wild-type trajectories and two ΔwaaF trajectories. Trajectory coordinates were saved every 0.2 ns for analysis. Each system was simulated for 5 μs. Before analysis, global translation in the membrane plane was removed by aligning each trajectory to the combined center of mass of all LPS molecules.
Trajectory processing and analysis were performed using custom Tcl and Python scripts together with VMD75. Nearest-neighbor calculations were performed in Python using SciPy76, and figures were generated using Python.
Hydrogen bonds between LPS molecules were analyzed using VMD. For each LPS molecule, neighboring LPS molecules were identified by selecting molecules containing at least one atom within 4 Å of the reference LPS. Hydrogen bonds were then detected using a donor–acceptor distance cutoff of 3.5 Å and a donor–hydrogen–acceptor angle cutoff of 30°. Both donor–acceptor directions were evaluated to capture hydrogen bonds in which the reference LPS acted as either donor or acceptor. Hydrogen-bond counts were averaged over the final 1 μs of each trajectory (Fig. 3a,b).
To estimate lateral diffusion coefficients, we calculated the two-dimensional mean-squared displacement (MSD) of the LPS center of mass in the membrane plane. MSD was calculated separately for five consecutive 1-μs intervals within each trajectory, with the reference coordinates reset at the beginning of each interval at 0, 1, 2, 3, and 4 μs. For each interval, the MSD was averaged over all 34 LPS molecules and fitted using a linear function. The diffusion coefficient was calculated as one-quarter of the fitted MSD slope, assuming two-dimensional diffusion. Because the trajectories primarily sampled local motion within a confined regime rather than long-range diffusion, these values should be interpreted as effective diffusion estimates over the simulated timescale (Fig. S4b,c).
To quantify local LPS mobility, we calculated the root-mean-square fluctuation (RMSF) of the lipid A center of mass in the membrane plane during the final 1 μs of each trajectory. Global translation was removed using the combined center of mass of all LPS molecules. RMSF was calculated separately for each LPS molecule and compared between wild-type and ΔwaaF systems (Fig. 3e,f).
To quantify LPS packing, we calculated local and global sixfold bond-orientational order parameters from the two-dimensional lipid A center-of-mass positions. Periodic boundaries in the membrane plane were accounted for when calculating intermolecular distances. For each LPS molecule , the six nearest neighboring LPS molecules were identified, and the hexatic order parameter was calculated as
where is the angle between the vector connecting LPS to neighbor and a fixed axis in the membrane plane. The magnitude ranges from 0 to 1, with values approaching 1 indicating that the six neighbors are arranged close to ideal hexagonal symmetry. Mean local order was calculated by averaging over all LPS molecules in each frame:
For per-LPS comparisons, local order was averaged over frames during the final 1 μs of each trajectory for each LPS molecule, yielding the time-averaged local order (Fig. 3h). Global hexatic order was calculated as
where is the number of LPS molecules. In contrast to mean local order, which measures the degree of hexagonal organization within individual neighborhoods, global order is sensitive to common orientational alignment across the entire LPS layer. Time courses were calculated over the full trajectories, and distributions used for comparison were obtained from the final 1 μs of each simulation (Fig. 3g-i, S4d).
To quantify the persistence of local LPS coordination, we calculated a nearest-neighbor retention function from the two-dimensional lipid A center-of-mass positions. Periodic boundaries in the membrane plane were included in all nearest-neighbor searches. For each LPS molecule , the six nearest neighbors at the first analyzed frame were defined as the initial neighbor set . At each subsequent time point, the six nearest neighbors were recalculated to obtain . The fraction of initial neighbors retained at time was calculated as
The neighbor-retention function was obtained by averaging over all LPS molecules. A value of 1 indicates complete preservation of the initial coordination shell, whereas decreasing values indicate progressive neighbor exchange and lateral rearrangement (Fig. 3j).
Mean interaction energies were calculated using the NAMD Energy plugin, considering the electrostatic and van der Waals interactions between each LPS molecule and its nearest neighbors (Supplementary Movies S1–S4). In this analysis, each LPS was treated as a distinct molecular unit, including any divalent cations within 4 Å due to their role in stabilizing intermolecular interactions. Because hydrogen bonds are not treated as a separate term in this calculation, their contributions are implicitly included within the electrostatic component.
Similarly, pairwise interaction energies were calculated between each LPS molecule and every other LPS in the membrane, again including nearby divalent cations within 4 Å in each LPS selection. These data were used to construct time-resolved inter-LPS interaction networks (Supplementary Movies S5–S8).
To quantify divalent-cation association with LPS, we counted Mg2+ and Ca2+ ions located within 4 Å of each LPS molecule in every analyzed frame during the final 1 μs of each trajectory. Counts were averaged over time separately for each LPS molecule, producing one mean cation-association value per LPS molecule for comparison between systems (Fig. 3c,d).
Supplementary Material
Acknowledgements
The authors thank members of the Huang lab for helpful discussions. This work was supported by a Stanford Interdisciplinary Graduate Fellowship (to J.S.), NIH Awards RM1 GM135102 (to K.C.H.) and R01 GM148586 (to J.C.G.), and NSF Award EF-2125383 (to K.C.H.). K.C.H. is a Chan Zuckerberg Biohub Investigator. This work was also supported in part by the National Science Foundation under Grant PHYS-1607611 and by the hospitality of the Aspen Center for Physics.
Data and code availability
All data used for generating figures in this study are available at a Stanford Digital Repository: https://purl.stanford.edu/gg071dr7283.
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Associated Data
This section collects any data citations, data availability statements, or supplementary materials included in this article.
Supplementary Materials
Data Availability Statement
All data used for generating figures in this study are available at a Stanford Digital Repository: https://purl.stanford.edu/gg071dr7283.
